US7321426B1 - Optical metrology on patterned samples - Google Patents
Optical metrology on patterned samples Download PDFInfo
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- US7321426B1 US7321426B1 US10/859,637 US85963704A US7321426B1 US 7321426 B1 US7321426 B1 US 7321426B1 US 85963704 A US85963704 A US 85963704A US 7321426 B1 US7321426 B1 US 7321426B1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/17—Systems in which incident light is modified in accordance with the properties of the material investigated
- G01N21/21—Polarisation-affecting properties
- G01N21/211—Ellipsometry
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/84—Systems specially adapted for particular applications
- G01N21/8422—Investigating thin films, e.g. matrix isolation method
Definitions
- the invention relates to the field of metrology, and in particular to computationally efficient optical metrology systems.
- Optical metrology tools determine the attributes of thin films in integrated circuits (ICs) by reflecting a probe beam of light off of the thin films. Data measurements from the reflected beam are collected and compared to an optical model of the thin films and any interfacing structures to generate values for the thin film attribute(s) of interest.
- optical metrology is performed on thin films formed on predetermined target regions of a wafer. Those target regions have historically included thin films formed on uniform (monolithic) base layers.
- monolithic targets i.e., targets located over monolithic base layers
- patterned targets i.e., targets located over patterned (non-monolithic) base layers.
- a patterned base layer is a grating base layer that can include periodic structures (e.g., lines), which can be formed from metal, silicon, or any other material used in an IC.
- a patterned base layer allows a metrology operation to be performed on a thin film that more closely resembles the physical, chemical, and mechanical properties of thin film portions in the active device area of the wafer.
- CMP chemical-mechanical polishing
- the soft metal deforms under the CMP slurry load.
- This dishing can significantly affect the accuracy of any optical metrology techniques used in the region. The softer the metal, the more this problem is amplified, and the more measurement accuracy is degraded. Since a large proportion of a patterned base layer is formed from semiconductor materials (i.e., the metal lines are typically formed in an oxide layer), it is less susceptible to dishing.
- grating targets can beneficially enhance the quality of optical metrology.
- Conventional methods for performing optical metrology on grating targets typically involve the same methodology used for metrology on monolithic targets. Specifically, a theoretical model (i.e., a set of equations based upon fundamental optical principles) is created for the grating target. The theoretical model is then used to determine values for the thin film “attribute of interest” (AOI, the thin film attribute for which an output value is desired). This process is described in greater detail with respect to FIGS. 1A-1D .
- AOI attribute for which an output value is desired
- a theoretical model C(TH) is generated for the test sample.
- This model can be created by, for example, solving the fundamental Fresnel equations that define the behavior of the probe beam at the test sample.
- measurement data D(MEAS) for the test sample is collected (often across a range of wavelengths or across a range of incident angles for ellipsometry or reflectometry).
- Measurement data D(MEAS) can be any ellipsometry measurement parameter, such as ⁇ , ⁇ , ⁇ , or ⁇ , or any reflectometry measurement parameter, such as reflectivity ( ).
- FIGS. 1A-1D This sequence of operations depicted in FIGS. 1A-1D is summarized in the flow diagram of FIG. 1E .
- a “DEFINE FUNDAMENTAL EQUATIONS” step 110 a set of equations that define the behavior of the probe beam at the test sample (e.g., Fresnel equations) are specified.
- a “GENERATE THEORETICAL MODEL” step 120 the fundamental equations defined in step 110 are solved to create a theoretical model for the test sample. Steps 110 and 120 therefore correspond to FIG. 1A .
- a “COLLECT MEASUREMENT DATA” step 130 the reflected probe beam data is gathered, as shown in FIG. 1B .
- the theoretical model is then regressed along the AOI(s) to match the measured data in a “REGRESS MODEL EQUATIONS” step 140 .
- a value(s) for the AOI(s) of the thin film layer is derived from the regressed model equations.
- an ellipsometry tool measures the ellipsometric angles ⁇ and ⁇ , where tan( ⁇ ) is the relative amplitude ratio of the incident and reflected probe beams, while ⁇ is the relative phase shift between the incident and reflected probe beams.
- Fresnel reflection coefficients R p and R s are complex functions of the wavelength(s) and angle(s) of incidence of the probe beam, and also of the optical constants (e.g., index of refraction, extinction coefficient) of the materials in the film stack.
- Specific functions for Fresnel reflection coefficients Rp and R s can be defined as sets of model equations that are associated with the individual layers making up the film stack.
- Equation 2 can be used to define a lower reflectance equation for each layer of the film stack. This results in a first set of reflectance equations for light polarized in the parallel direction (based on Equations 2 through 8) and a second set of reflectance equations for light polarized in the perpendicular direction (based on Equations 2 through 7 and 9).
- the ambient environment is defined as the topmost “layer” in the film stack
- the lower reflectance equation for that ambient layer is equivalent to Fresnel reflection coefficients Rp and Rs, respectively. Therefore, by solving the first and second recursive sets of reflectance equations, the model equations for the film stack can be fully defined.
- each of the two sets of reflectance equations is a recursive set.
- the reflectance at the substrate is defined to be zero, which provides a starting point from which both sets of recursive reflectance equations can be solved.
- the patterned base layer can be treated as a solid layer, thereby simplifying the model equations.
- the model equations could also be simplified by ignoring phase information and only using reflected intensity data in the calculations. However, in either case, the approximations can result in unacceptable inaccuracy in the final measurement values.
- the invention provides a system and method for accurately measuring attributes (e.g., thickness, index of refraction, coefficient of extinction, surface roughness, composition) of a thin film(s) formed on a patterned base layer by creating an empirical optical model for the test sample.
- attributes e.g., thickness, index of refraction, coefficient of extinction, surface roughness, composition
- the invention beneficially eliminates the need for the complex and resource-intensive computation of accurate theoretical models of the film stack.
- the invention applies to any optical metrology tool that can be used to measure one or more thin films formed on a patterned structure, including reflectometry tools (which measure/detect changes in reflected intensity) and ellipsometry tools (which measure/detect changes in reflected intensity and phase).
- the optical metrology tool can make measurements at a single angle of incidence and/or wavelength, or can make measurements at multiple angles of incidence and/or wavelengths.
- the empirical model can be created by selecting an expected model equation form (i.e., a specified set of terms and coefficients), and then regressing the coefficients of that expected form until outputs are generated that adequately match a set of experimental data.
- an expected model equation form i.e., a specified set of terms and coefficients
- the coefficients of the expected model form will typically be functions of wavelength and/or angle of incidence. Therefore, at every wavelength and/or angle of incidence, a new set of coefficients will be determined. However, the computational cost of generating these multiple sets of coefficients is still orders of magnitude less than the computational cost of actually solving the theoretical equations for a grating-based thin film stack. Note further that different model equations can be provided for different expected attribute ranges to improve the accuracy of the output values.
- the empirical optical model can be generated by compiling sets of data taken at various values of the attribute(s) of interest. For example, reflectivity measurements could be taken from a number of different grating targets having different thin film thicknesses (i.e., thickness is the attribute of interest). These measurements could then be compiled into an empirical lookup model. By interpolating the data in the empirical lookup model to match measured data from a test sample, an output value for the attribute of interest can be generated.
- the empirical optical model can be generated by compiling sets of grating factor values that, when applied to the standard monolithic base layer model equations, compensate for the optical effects of the grating base layer. By interpolating the grating factor values until the (adjusted) model output matches data from a test sample, an output value for the attribute of interest of the test sample can be generated.
- FIGS. 1A-1D are stages in a conventional method for measuring attributes for a thin film formed on a grating.
- FIG. 1E is a flow diagram of a conventional method for measuring attributes for a thin film formed on a grating.
- FIG. 2 is a schematic diagram of an optical measurement system that includes model approximation logic, according to an embodiment of the invention.
- FIG. 3 is a flow diagram of a method for determining thin film attributes using an empirical model, according to an embodiment of the invention.
- FIG. 4 is a wafer that includes both grating targets and monolithic targets, according to an embodiment of the invention.
- FIG. 5 is a flow diagram of a method for determining thin film attribute values using an empirical model, according to an embodiment of the invention.
- FIGS. 6A-6F are stages in a method for determining thin film attribute values using an empirical model, according to an embodiment of the invention.
- FIG. 7 is a flow diagram of a method for determining thin film attribute values using a lookup model, according to an embodiment of the invention.
- FIGS. 8A-8D depict a method for determining thin film attribute values using a lookup model, according to an embodiment of the invention.
- FIGS. 9A-9D depict a method for determining thin film attribute values using a lookup model, according to another embodiment of the invention.
- FIG. 10 is a flow diagram of a method for determining thin film attribute values using an empirical model, according to another embodiment of the invention.
- FIGS. 11A-11G depict a method for determining thin film attribute values using a grating factor lookup model, according to another embodiment of the invention.
- FIG. 2 shows an optical metrology system 200 for determining values for one or more AOIs (i.e., attributes of interest, such as thickness, index of refraction, roughness, and composition, among others) of a test sample 290 , according to an embodiment of the invention.
- Optical metrology system 200 includes a beam source 210 , input optics 220 , output optics 230 , a detector 240 , and data processing resources 250 .
- test sample 290 includes a patterned base layer 292 formed on a substrate 291 , and a thin film 293 formed on patterned base layer 292.
- Patterned base layer 292 includes a series of lines 292 - 1 (e.g., metal lines) formed in a base material 292 - 2 . Note that while patterned base layer 292 is depicted as a patterned base layer for exemplary purposes, patterned base layer 292 can include any type of patterning. Note further that thin film 293 can be made up of any number of material layers.
- a probe beam 211 generated by beam source 210 is directed onto thin film 293 by input optics 220 .
- a resulting reflected beam 212 is directed by output optics 230 onto detector 240 , and the measurements taken by detector 240 are processed by data processing resources 250 to determine values for the desired parameters of thin film 293 (e.g., thickness, index of refraction, or composition).
- beam source 210 , input optics 220 , output optics 230 , and detector 240 can comprise any types of components that are appropriate for the particular metrology technique employed by optical metrology system 200 .
- beam source 210 could comprise a laser or arc lamp
- input optics 220 could comprise a polarizer, monochromator, compensator, and/or focusing optics
- output optics 230 could comprise a polarizer, analyzer, and/or focusing optics
- detector 240 could comprise a photodiode or charge-coupled device (CCD) array.
- CCD charge-coupled device
- beam source 210 could comprise a halogen or deuterium lamp
- input optics 220 could comprise a beamsplitter, monochromator, and/or focusing optics
- output optics 230 could comprise a prism, diffraction patterned, and/or focusing optics
- detector 240 could comprise a camera or CCD/photodiode array.
- data processing resources 250 includes model approximation logic 251 (i.e., empirical model generation logic) and regression logic 252 .
- Model approximation logic 251 creates an empirical optical model of the thin film stack using experimental data. Unlike a theoretical model, which is based on general physical laws, an empirical model is at least in part based on experimental or observed data. Therefore, an empirical model can be created without solving the complex set of equations required for a theoretical model, thereby minimizing the computing power requirements of data processing resources 250 .
- FIG. 3 shows a flow diagram for an optical metrology operation incorporating an empirical model, in accordance with an embodiment of the invention.
- experimental data e.g., optical metrology measurement data such as ellipsometric angles tan( ⁇ ) and ⁇ , or reflectance
- This experimental data is taken from a target location on the calibration sample that includes a thin film over a patterned base layer (e.g., thin film 293 and patterned base layer 292 shown in FIG. 2 ).
- the experimental data is then used to generate an empirical model in a “MODEL APPROXIMATION” step 320 .
- data can refer either to standard metrology data types such as ellipsometric angles tan( ⁇ ) and ⁇ , or reflectance R, or to the raw data from the measurement tool (e.g., CCD counts or other electrical signals).
- the invention can be applied to any type of data. Because all metrology tools perform processing operations on metrology data types (conversion from raw data to metrology data is performed immediately by the metrology tool), the exemplary descriptions presented herein are described with respect to metrology data types, rather than raw data types.
- the expected value(s) of the AOI(s) (along with the other thin film attribute values) must either be reasonably well known, or else must be explicitly measured.
- the thickness of thin film 293 must be a defined value during “MODEL APPROXIMATION” step 320 .
- the process used to form thin film 293 will be well characterized enough that an expected thickness value for thin film 293 will provide sufficient accuracy to generate the empirical model.
- This measured thickness can be determined by applying conventional optical metrology techniques to one or more monolithic targets that are located on the same test sample as the patterned target(s). The closer the monolithic targets are to the patterned targets, the more closely the measured thin film thickness at the monolithic targets will match the thin film thicknesses at the patterned targets.
- FIG. 4 shows a wafer (calibration sample) 490 in accordance with an embodiment of the invention.
- Wafer 490 includes multiple patterned targets 491 and multiple monolithic targets 492 , with each monolithic target 492 being located in close proximity to a patterned target 491 . Therefore, the thin film attribute(s) measured at the monolithic targets 492 using conventional metrology techniques can be used when generating the empirical model(s) for the patterned-based targets.
- a wafer in accordance with the invention can include any number patterned and monolithic targets in any arrangement.
- the expected/measured value(s) of the AOI(s) are used in conjunction with the experimental data to generate an empirical model of the patterned target location.
- This empirical model can be either a mathematical model (set of equations) or a lookup model (an indexed set of data, equations, or grating factors), both of which are described in greater detail below. In either case, the complex theoretical modeling of the patterned target location is avoided, thereby greatly simplifying model generation.
- the empirical model can then be used to determine values for the AOIs of test samples, so long as the base layer(s) at the patterned target(s) of the test sample(s) is substantially similar to the patterned base layer(s) of the calibration sample(s) used to generate the empirical model.
- a “COLLECT MEASUREMENT DATA” step 330 measurements are taken at the patterned targets of a test sample(s) to be measured.
- the empirical model generated in step 320 is fitted to the measurement data, i.e., the empirical model is either regressed or interpolated along the AOI(s) until the output of the empirical model matches the measurement data.
- the “matching” of the empirical model output and the measurement data is based on a predetermined error threshold (tolerance band) that defines a desired degree of correlation between the regressed model and the measurement data.
- step 350 the attribute value(s) determined during step 340 are output as the calculated value(s) for the AOI(s). To perform additional measurements on additional test samples, the process can then loop back to step 330 .
- FIG. 5 shows a detailed embodiment of the flow chart of FIG. 3 , including sub-steps specific to the use of an experimental empirical model, according to an embodiment of the invention.
- “COLLECT EXPERIMENTAL DATA” step 310 - 1 begins with a “COLLECT PATTERNED BASE DATA” step 311 in which experimental data is gathered from one or more patterned targets. Measurements can then be taken at one or more monolithic targets (e.g., monolithic targets 492 in FIG. 4 ) in an optional “COLLECT MONOLITHIC BASE DATA” step 312 to provide actual values for the AOI(s) of the patterned targets (e.g., patterned targets 491 in FIG.
- step 312 can be skipped.
- “MODEL APPROXIMATION” step 320 - 1 begins with a “SPECIFY MODEL FORM” step 321 , in which an expected mathematical form for the final empirical model is defined.
- This expected form can be based on any information related to the metrology operation being performed and the experimental data collected in step 310 - 1 .
- the expected mathematical form could be based on known theoretical models of similar systems.
- the expected mathematical form of the model equations could be selected according to the shape of the experimental data.
- a “smooth” form e.g., polynomial
- a graph of the experimental data gathered in step 311 exhibits smooth behavior (small number of peaks and valleys) relative to the independent measurement parameter (e.g., wavelength or angle of incidence).
- the independent measurement parameter e.g., wavelength or angle of incidence.
- a non-smooth form e.g., oscillating function
- a polynomial form could always be selected (at least initially), in an effort to maintain simplicity.
- the expected mathematical form for the model equations could be generated by applying special correction factors to the standard (theoretical) mathematical form(s) for monolithic base layer structures.
- correction factors can include “grating factors” (i.e., factors that represent the effects of the grating layer(s)) and “space fill factors” (i.e., factors that represent the relative contributions from the grating elements and the filler material between grating lines).
- a set of standard recursive equations (e.g., a set of lower reflectance equations generated using Equations 1-10) can be defined for the layers in the film stack, but with grating factors applied where a grating layer is present, the grating factors compensating for the optical effects of the grating layer.
- the compensation provided by the grating factors can be enhanced by separating a grating layer into a “grating line” portion (i.e., the periodic lines that form the actual grating pattern) and a “space fill” portion (i.e., the filler material between the grating lines).
- a space fill factor can be applied to the model equations to adjust for the relative proportions of grating lines and space fill portions in the grating layer.
- the standard monolithic layer model equation (s) can be converted into an adjusted model equation (s) that is representative of the optical behavior of the grating layer.
- a grating factor g can be defined that represents the patterned layer (grating structure) optical effects
- a space fill factor f can be defined that represents and the relative contributions of the grating line and space fill portions (e.g., the fraction of the grating layer occupied by the space fill material).
- adjusted equations 10a and 10b resolve to the standard monolithic base layer reflectance model equations (i.e., equations for a film stack formed on a monolithic base layer).
- grating factors g p and g s can themselves take almost any form, depending on the desired accuracy to be provided by the adjusted model equations.
- the grating factors can be defined as constants.
- grating factors g p and g s can be defined as functions of the independent measurement parameter (e.g., wavelength or angle of incidence).
- the grating factors can even be functions of one or more of the attributes of interest (e.g., grating factors g p and g s can be functions of the thickness of the layer of interest).
- equations 10a and 10b represent a monolithic layer formed on a grating layer, with grating factors being used to adjust the grating line-thin film interface reflectance to compensate for the non-monolithic nature of the grating layer.
- This adjusted reflectance i.e., the term “g p +(1+g p )*R BGL (j)” in Equation 10a or the term “g s +(1 ⁇ g s )*R BGL (j)” in Equation 10b
- R BSF (j) space fill factor
- space fill factor f i.e., a weighted average is performed on the two terms with space fill factor f as the weighting factor.
- R BGL (j) and R BSF (j) are simply represented using Equation 2, described above.
- R FGL (j) interface Fresnel reflectance
- R FGL (j) is given by the following:
- R FGL ( j ) ( p ( j ) ⁇ p GL ( j ⁇ 1))/( p ( j )+ p GL ( j ⁇ 1)) [15]
- p(j) and p GL (j ⁇ 1) represent dispersion factors for layer j and a grating line of layer j ⁇ 1, respectively.
- Dispersion factor p(j) would be given by Equations 8 and 9 above, for light polarized in the parallel and perpendicular directions, respectively.
- Equation 11 providing the model equation for a layer(s) in the film stack formed on a grating layer
- Equation 2 providing the model equations for the layers in the film stack that are not formed on a grating layer.
- the reflectance terms in Equations 10a and 10b could be replaced with transmittance terms for reflectometry measurements.
- the lower reflectance term R BGL (j) for the thin film-grating line interface in Equations 10a and 10b could be replaced with lower transmittance term F BGL (j) for the thin film-grating line interface, indicated by the following:
- F BLG ⁇ ( j ) ( p ⁇ ( j ) + p GL ⁇ ( j - 1 ) 2 ⁇ P ⁇ ( j ) ) ⁇ ( 1 + R FGL ⁇ ( j ) * R TGL ⁇ ( j - 1 ) ) * F TGL ⁇ ( j - 1 ) [ 18 ]
- p(j) and p GL (j ⁇ 1) represent dispersion factors for layer j and a grating line of layer j ⁇ 1, respectively
- R FGL (j) is the interface Fresnel reflectance between layer j and a grating line in layer j ⁇ 1
- R TGL ( j ⁇ 1) is the reflectance at the top of the grating line in layer j ⁇ 1
- F TGL (j ⁇ 1) is the transmittance at the top of the grating line in layer j ⁇ 1, just as described above with respect to Equation 12.
- the lower reflectance term R BSF (j) for the thin film-space fill interface in Equation 12 could be replaced with lower transmittance term F BSF (j) for the thin film-space fill interface.
- the space fill lower transmittance term F BSF (j) would be defined in much the same manner as described above for grating line lower transmittance term F BGL (j). Note that when solving the recursive transmittance equations, the transmittance at the substrate is defined to be zero (in contrast to the substrate reflectance, which is equal to one, as noted above).
- the coefficients of that expected mathematical form are adjusted according to the experimental data in a “REGRESS ALONG COEFFICIENTS” step 322 .
- variables in the model equations making up the expected mathematical form are set to an expected or measured (step 312 ) value(s).
- the model equations are regressed along their coefficients (e.g., grating factors g p and g s in Equations 10a and 10b, respectively).
- the model equation coefficients are fixed in a “FINALIZE MODEL EQUATIONS” step 323 to complete the empirical model.
- the empirical model is generated by simple regression, rather than by actually solving a set of equations, the empirical model can be created much more rapidly than can a conventional theoretical model.
- conventional optical metrology tools already include regression capabilities (for determining AOI output values from the theoretical model), conventional tools can be readily adapted to perform steps 321 - 323 to generate the empirical model.
- steps 330 , 340 , and 350 are substantially similar to what would be performed in a conventional metrology operation. The only difference is that the model regression in step 340 is performed on an empirical model, while a conventional metrology operation would perform the regression on a theoretical model. Therefore, the invention can be easily incorporated into existing metrology systems.
- FIGS. 6A-6E provide an exemplary depiction of the process described with respect to FIG. 5 .
- data processing resources 250 - 1 gathers experimental data D_EXP at a known value T 1 of a thin film attribute of interest T (corresponding to step 311 in FIG. 5 ).
- T 1 a thin film attribute of interest T
- delta and wavelength could be replaced with any other optical metrology measurement parameters (e.g., reflectance and angle of incidence).
- expected mathematical form MF_EXP is defined in model approximation logic 251 - 1 (step 321 ).
- expected mathematical form MF_EXP is a function of attribute variable T, and includes coefficients A, B, and C.
- expected mathematical form MF_EXP can be entered by a user via an interface to data processing resources 250 - 1 (e.g., a graphical user interface or a command line interface).
- a user could select expected mathematical form MF_EXP from a group of mathematical forms stored in data processing resources 250 - 1 or stored at a remote location.
- known value T 1 (either an expected value or a measured value from step 312 ) is substituted into the empirical model form MF_EXP(T,A,B,C).
- Empirical model form M_EXP(T1,A,B,C) is then regressed along coefficients A, B, and C (step 322 ) by regression logic 252 - 1 .
- empirical model form MF_EXP(T1,A1,B1,C1) matches experimental data D_EXP(T 1 ) (i.e., is within a predetermined tolerance band of experimental data D_EXP(T1)), as shown in FIG.
- coefficients A, B, and C are fixed at values A1, B1, and C1 (step 323 ) to finalize an empirical model M_EMP(T,A1,B1,C1). Note that if multiple sets of experimental data are present, simultaneous regression can be performed for each of the sets of experiments data, and the values of coefficients A, B, and C can be set when each of the regression outputs is within a predetermined tolerance band TOL of its associated experimental data.
- empirical model M_EMP(T,A1,B1,C1) is regressed along attribute T by regression logic 252 - 1 , as shown in FIG. 6D (step 340 ).
- the value T 2 of attribute T that causes empirical model M_EMP(T,A1,B1,C1) to match measurement data D_MEAS (i.e., generate an empirical model output that is within a predetermined tolerance band of measurement data D_MEAS), as shown in FIG. 6E can then be provided by data processing resources 250 - 1 as the output value of attribute T (step 350 ).
- the empirical model generated in FIG. 6C via regression can be used to perform optical metrology on any number of additional test samples.
- coefficients A, B, and C may be initially treated as constant and fixed at their respective predetermined values of A 1 , B 1 , and C 1 , respectively.
- coefficients A, B, and C could always be set to a predetermined nominal values that would result in zero correction to the nominal reflectance as computed for a film stack with grating factors g p and g s equal to zero.
- additional refinement of the regression process can be achieved by allowing the regression logic to regress with AOI T held at its predetermined value of T2. In doing so, the quality of fit can be improved.
- simultaneous regression of AOI T (from the predetermined value of T2) with coefficients A, B, and C can be performed to generate a new empirical model M_EMP(T 3 , A 2 , B 2 , C 2 ), as shown in FIG. 6F .
- This can result in a new value T 3 for AOI T that improves the match with measurement data D_MEAS, thereby providing improved measurement quality.
- an empirical model can be created as a lookup model by compiling multiple sets of experimental data.
- FIG. 7 shows a detailed embodiment of the flow chart of FIG. 3 , including sub-steps specific to the use of an empirical lookup model, according to an embodiment of the invention.
- a “COLLECT EXPERIMENTAL DATA” step 310 - 2 (corresponding to step 310 in FIG. 3 ) begins with a “COLLECT MULTIPLE PATTERNED BASE DATA SETS” step 311 in which experimental data sets are gathered from multiple patterned targets.
- the multiple patterned targets include at least two patterned targets for which the values for an AOI(s) are different.
- the multiple patterned targets can be included in a single test sample, with differing process parameters at each patterned target providing the desired attribute value variations.
- patterned target measurements can be taken from multiple test samples to provide the desired number of different values for the AOI(s).
- step 312 actual values for those various attributes of interest can be determined in an optional “COLLECT MULTIPLE MONOLITHIC BASE DATA SETS” step 312 , in which measurements of those attributes of interest are taken from monolithic targets (e.g., monolithic targets 492 in FIG. 4 ) in close proximity to the patterned targets (e.g., patterned targets 491 in FIG. 4 ).
- the thin film attribute values determined from measurements at the monolithic targets can then be used as the attribute values for the patterned targets.
- step 312 can be skipped.
- “MODEL APPROXIMATION” step 320 - 2 begins with a “CORRELATE DATA” step 325 , in which the experimental data set from each patterned target is correlated with the AOI value(s) for that patterned target.
- the experimental data sets are then compiled into a database with the AOI(s) as the lookup parameter(s) in a “COMPILE TABLE” step 326 , thereby creating the empirical lookup model.
- Increasing the number of data sets associated with different attribute values collected in step 311 can increase the resolution (if the different attribute values are closely spaced) or the range (if the different attribute values are widely spaced) of the lookup model.
- an empirical lookup model can be generated by substituting multiple different AOI values into an empirical mathematical model developed in the manner described above.
- measurement data is gathered from one or more patterned-based targets on a test sample having an unknown value(s) for the AOI(s) in a “COLLECT MEASUREMENT DATA” step 330 .
- the measured data is compared with the lookup model, which interpolates the data in the empirical lookup model for each wavelength and angle of incidence along the AOI(s) in a “SOLVE FOR ATTRIBUTE(S)” step 340 , and the calculated attribute value is output in an “OUTPUT ATTRIBUTE VALUE(S)” step 350 .
- step 340 can apply any desired interpolation algorithm, such as cubic spline interpolation or quadratic interpolation.
- the actual interpolation can be performed using the existing regression capabilities of an optical metrology tool, thereby simplifying the implementation of the invention.
- FIGS. 8A-8D provide an exemplary depiction of the process described with respect to FIG. 7 , according to an embodiment of the invention.
- data processing resources 250 - 2 gathers multiple experimental data sets D_EXP from patterned targets having different values of an AOI T (i.e., T 1 , T 2 , and T 3 ).
- T 1 , T 2 , and T 3 an AOI T
- delta and wavelength could be replaced with any other optical metrology measurement parameters (e.g., reflectance and angle of incidence).
- Experimental data sets D_EXP(T1), D_EXP(T2), and D_EXP(T3) are then compiled into an empirical lookup model DB_EMP-2 by model approximation logic 251 - 2 in FIG. 8B (step 320 - 2 ). Then, in FIG. 8C , a new set of measurement data D_MEAS is taken from a new test sample (step 330 ), and the data in the lookup model is interpolated by regression logic 252 - 2 to determine a value for the AOI(s). Various methods of interpolation will be readily apparent.
- the experimental data sets in a lookup model can be used to define a measurement function at each wavelength.
- the measurement value (A in this case) can be represented as a function of the AOI.
- the value of ⁇ can be represented by functions f( ⁇ 1 ,T), f( ⁇ 2 ,T), and f( ⁇ 3 ,T), respectively. Then, by interpolating along the AOI in those functions as shown in FIG.
- a set of interpolated values for AOI T can be determined at each wavelength (e.g., values T 4 , T 5 , and T 6 at wavelengths ⁇ 1 , ⁇ 2 , and ⁇ 3 ).
- a final output value for AOI T can then be determined from this set of interpolated values T 4 , T 5 , and T 6 by various methods, including averaging the values, selecting the median value, or performing a weighted average, among others.
- simultaneous global interpolation may be employed for a set of functions (e.g., f( ⁇ 1 ,T), f( ⁇ 2 ,T), and f( ⁇ 3 ,T)) via regression on the AOI (T in this case).
- a set of functions e.g., f( ⁇ 1 ,T), f( ⁇ 2 ,T), and f( ⁇ 3 ,T)
- a final output value for AOI T e.g., T 7
- FIGS. 9A-9D provide an exemplary depiction of the process described with respect to FIG. 7 , according to another embodiment of the invention.
- data processing resources 250 - 3 gathers multiple experimental data sets D_EXP(T) from patterned targets having different values of an AOI T (i.e., T 1 , T 2 , and T 3 ).
- an AOI T i.e., T 1 , T 2 , and T 3
- delta and wavelength could be replaced with any other optical metrology measurement parameters (e.g., reflectance and angle of incidence).
- Empirical lookup model DB_EMP-3 is simply a collection of reference data points, each of which represents the AOI value for a particular set of measurement parameters (in this case, for a particular wavelength/delta combination).
- all the reference data points derived from an experimental data set D_EXP(T 1 ) will represent wavelength/delta combinations corresponding to an AOI value of T 1 —e.g., reference data points P( ⁇ 1 , ⁇ 1 , T 1 ), P( ⁇ 2 , ⁇ 2 , T 1 ), and P( ⁇ 3 , ⁇ 3 , T1).
- empirical lookup model DB_EMP-3 is a data point-based model, unlike empirical lookup model DB_EMP-2 described with respect to FIG. 8B , which is made up of a set of functions.
- a new set of measurement data D_MEAS is taken from a new test sample (step 330 ) and is compared to the reference data points of empirical lookup model DB_EMP-3.
- the reference data points that match measurement data D_MEAS e.g., are within a predetermined tolerance band of measurement data D_MEAS
- FIG. 9D is determined in FIG. 9D , as indicated by the circled reference data points (e.g., reference data points P( ⁇ 1 , ⁇ 4 , T 2 ), P( ⁇ 2 , ⁇ 5 , T 3 ), and P( ⁇ 3 , ⁇ 6 , T 4 ).
- empirical lookup model DB_EMP provides a simple means for providing optical metrology for patterned-based thin film layers.
- the lookup model can be based on grating factors (correction factors that compensate for grating base layer-induced deviations from the monolithic base layer results), rather than measured data.
- the lookup model instead of creating the lookup model by simply compiling the raw experimental data measured from each patterned target, the lookup model could be created by converting that raw experimental data into grating factors associated with the patterned targets.
- FIG. 10 shows a detailed embodiment of the flow chart of FIG. 3 , including sub-steps specific to the use of a grating factor lookup model, according to an embodiment of the invention.
- a “COLLECT EXPERIMENTAL DATA” step 310 (which is substantially similar to steps 311 and 312 described with respect to FIGS. 5 and 7 ), experimental data sets are gathered from multiple patterned targets.
- the multiple patterned targets can include thin film layers having different attribute of interest values, formed on patterned base layers having substantially the same geometries.
- the multiple patterned targets can include thin film layers having different attribute of interest values formed on patterned base layers having different geometries.
- the experimental data can be gathered from a single tool or multiple tools.
- the effects of noise i.e., measurement variability
- the effects of noise in a particular tool can be compensated for by taking repeat measurements using the same calibration test sample(s).
- the experimental data gathered from the multiple measurements can then either be averaged or used as independent experimental data sets, thereby reducing the effects of random measurement variations generated within the particular metrology tool.
- the effects of systemic measurement variability among a group of metrology tools can be reduced by taking measurements from the same calibration test sample(s) from all of the metrology tools in the group. Then, by incorporating the experimental data from each of the metrology tools into the subsequently derived empirical model, the empirical model is effectively matched to all the tools, rather than being overly biased towards any one tool (i.e., the same empirical model can be used with any of the metrology tools, thereby eliminating the need to generate a different model for each tool).
- either of the aforementioned techniques i.e., multiple measurements of the same calibration test sample(s) using a single toll, and measurements of the same calibration test sample(s) using multiple tools
- the techniques can also be applied during the experimental data collection steps described with respect to FIGS. 3 , 5 , and 7 .
- the techniques can be applied to any metrology tool or group of metrology tools in which modeling based on experimental data is used.
- “MODEL APPROXIMATION” step 320 - 3 begins with a “DERIVE GRATING FACTORS” step 1021 , in which the adjusted model equations for the patterned targets (e.g., adjusted model equations 10a and 10b) are solved using the experimental data sets to generate a set of values for the grating factors (e.g., grating factors g p and g s ).
- the grating factors are correction factors that adjust the standard (monolithic base layer) equations to compensate for the optical effects introduced by the patterned base layer(s).
- the grating factors can take any form (e.g., constant, polynomial, sine wave or oscillator function), depending on desired accuracy of the compensation provided by those grating factors.
- the grating factor values can comprise discrete values or continuous functions.
- the grating factor values are then compiled into a lookup model in a “CREATE GRATING FACTOR MODEL” step 1022 . Note that the particular structure of this grating factor lookup model depends on the form of the grating factors themselves.
- each grating factor can comprise a function of the independent measurement parameter (e.g., wavelength or angle of incidence) that is specific to a particular combination of patterned base layer geometry (e.g., grating line size, proportion of grating line to filler material) and attribute of interest value(s).
- the grating factor model can then comprise a multidimensional table, wherein the specific table dimension depends on the number of different AOIs and patterned base layer geometries.
- each different patterned base layer geometry will be associated with its own set of grating factor values. For example, if the experimental data is taken from patterned targets having two different patterned base layer geometries, then certain grating factor values derived from that experimental data will be associated with one base layer geometry and other grating factor values will be associated with the other base layer geometry.
- any particular patterned base layer geometry can be contained within the grating factor values associated with that patterned base layer geometry, the actual base layer geometry details need not be known. Because the different patterned base layer geometries are simply used as identifiers (labels) to segregate the various grating factor values, the geometry details are not critical.
- the adjusted model equations include a space fill factor to account for grating line dimensions (e.g., space fill factor f described with respect to equations 10a and 10b), that space fill factor need not be strictly accurate, so long as a different space fill factor is used for each different base layer geometry.
- measurement data is gathered from one or more patterned-based targets on a test sample having an unknown value(s) for the AOI(s) in “COLLECT MEASUREMENT DATA” step 330 .
- the measured data is compared with the lookup model, which interpolates the data in the empirical lookup model for each wavelength and angle of incidence along the AOI(s) in a “SOLVE FOR ATTRIBUTE(S)” step 340 - 3 .
- step 340 - 3 an initial test value(s) for the AOI(s) is selected in a “SELECT AOI VALUE(S)” step 1041 . Then, in “SELECT GC” step 1042 , the set of grating factor values associated with the patterned base layer geometry of the measurement data is determined. Note that if only a single patterned base layer geometry is used, then step 1042 need not be performed.
- a “GRATING FACTOR INTERPOLATION” step 1043 the set of grating factor values selected in step 1042 are interpolated along the AOI(s) to match the test AOI value(s) selected in step 1041 , thereby generating a test grating factor(s) (as noted above, measurement data from a single target can be associated with multiple sets of grating factor values—e.g., grating factors g s and g p for p-polarized and s-polarized light, respectively). Note that while extrapolation could also be used to determine the test grating factor(s), extrapolation is inherently more prone to inaccuracy than interpolation.
- a “MODELING” step 1044 the test grating factor value(s) and the test AOI value(s) are substituted back in to the adjusted model equation (s) used to determine the grating factor value(s) in step 1021 .
- the resulting model output is compared to the actual measured data in a “MATCH?” step 1045 . If the model output (based on the test AOI value(s) and the test grating factor(s)) is outside a predetermined tolerance band of the measured data, the process loops back to step 1041 , where a new AOI value(s) is selected. Otherwise, the test AOI value(s) is provided as the output AOI value(s) for the test sample in “OUTPUT ATTRIBUTE VALUE(S)” step 350 .
- FIGS. 11A-11G provide an exemplary depiction of the process described with respect to FIG. 10 , according to an embodiment of the invention.
- data processing resources 250 - 3 gathers multiple experimental data sets D_EXP from patterned targets having different values of an AOI T (i.e., T 1 , T 2 , and T 3 ).
- FIGS. 11A-11G depict an operation based on a single AOI (thickness of a single thin film) and a single patterned base layer geometry (GC 1 ).
- the invention can be applied to systems involving multiple AOIs and multiple patterned base layer geometries.
- delta and wavelength could be replaced with any other optical metrology measurement parameters (e.g., reflectance and angle of incidence, respectively).
- Model values for grating factors g p i.e., g p (GC 1 ,T 1 ), g p (GC 1 ,T 2 ), g p (GC 1 ,T 3 )) and g s (i.e., g s (GC 1 ,T 1 ), g s (GC 1 ,T 2 ), g s (GC 1 ,T 3 )) are determined for data sets D_EXP(GC 1 ,T 1 ), D_EXP(GC 1 ,T 2 ), and D_EXP(GC 1 ,T 3 ) (step 1021 ), and are compiled into grating factor lookup models (step 1022 ) by model approximation logic 251 - 3 , as shown in FIGS.
- the lookup model associates each set of grating factor values with a specific patterned base layer geometry (GC 1 ) and an AOI value(s) (T 1 , T 2 , or T 3 ).
- Measurement data D_MEAS is taken from a patterned target having an unknown AOI value (TA) and substantially the same geometry (GC 1 ) as the patterned targets used to gather experimental data sets D_EXP(GC 1 ,T 1 ), D_EXP(GC 1 ,T 2 ), and D_EXP(GC 1 ,T 3 ) (shown for reference).
- TA unknown AOI value
- GC 1 substantially the same geometry
- a test value T 4 is selected for unknown AOI TA (step 1041 ), and the original model grating factor values g p (GC 1 ,T 1 )-g p (GC 1 ,T 3 ) and g s (GC 1 ,T 1 )-g s (GC 1 ,T 3 ) are interpolated (step 1043 ) along AOI T to derive test grating factors g p (GC 1 ,T 4 ) and g s (GC 1 ,T 4 ), respectively, that are associated with test value T 4 , as shown in FIGS. 11E and 11F , respectively. Note that since a single patterned base layer geometry is being used (GC 1 ), optional step 1042 described with respect to FIG. 10 is not performed.
- the interpolation (indicated by the vertical double-ended arrows) between model grating factor values g p (GC 1 ,T 1 )-g p (GC 1 ,T 3 ) and between model grating factors g s (GC 1 ,T 1 )-g s (GC 1 ,T 3 ) shown in FIGS. 11E and 11F , respectively, can be performed by regression logic 252 - 3 in an any manner.
- cubic spline interpolation or quadratic interpolation could be used to define values for g p (GC 1 ,T 4 ) and g s (GC 1 ,T 4 ) at each wavelength ⁇ (independent measurement parameter).
- Grating factor values g p (GC 1 ,T 4 ) and g s (GC 1 ,T 4 ) are then substituted into the adjusted model equations (originally used to derive the grating factor lookup models) to generate a test model output D_INT(GC 1 ,T 4 ), shown in FIG. 11G (step 1044 ).
- Test model output D_INT(GC 1 ,T 4 ) is compared against the test sample measured data D_MEAS(GC 1 ,TA) (step 1045 ), and if test model output D_INT(GC 1 ,T 4 ) is within a predetermined tolerance band TOL of measured data D_MEAS, AOI value T 4 is output as the value for the test sample AOI TA (step 350 ). Otherwise, the process loops back to the selection of a new test value T 4 and the generation of new test grating factors g p (GC 1 ,T 4 ) and g s (GC 1 ,T 4 ).
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Abstract
Description
tan(ψ)e iΔ =R p /R s [1]
where Rp and Rs are the complex Fresnel reflection coefficients at the surface of the film stack for light polarized parallel and perpendicular, respectively, to the plane of incidence.
R B(j)=(R F(j)+R T(j−1)/(1+R F(j)*R T(j−1)) [2]
where RB(j) is the reflectance at the bottom of layer j (“lower reflectance”), RF(j) is the interface Fresnel reflectance between layer j and layer j−1 (i.e., the layer immediately below layer j), and RT(j−1) is the reflectance at the top of layer j−1 (“upper reflectance”).
R T(j−1)=R B(j−1) exp(−4πi (n(j−1)d(j−1)cos(θ(j−1))/λ)) [3]
where RB(j−1) is the lower reflectance of layer j−1, n(j−1) is the index of refraction of layer j−1, d(j−1) is the thickness of layer j−1, and θ(j−1) is the angle of incidence of the probe beam as it enters layer j−1.
n(j−1)=A(j−1)+B(j−1)/λ2 +C(j−1)/λ4 [4]
where A(j−1), B(j−1), and C(j−1) are Cauchy coefficients for index of refraction that depend on the material properties of layer j−1 and the wavelength λ of the probe beam. Note that various other equations can be used to define index of refraction.
N(j−1)=n(j−1)+ik(j−1) [5]
where k(j−1) is the extinction coefficient for the appropriate material layer given by:
k(j−1)=D(j−1)+E(j−1)/λ2 +F(j−1)/λ4 [6]
where D(j−1), E(j−1), and F(j−1) are Cauchy coefficients for extinction that depend on the material properties of layer j−1 and the wavelength λ of the probe beam.
R F(j)=(p(j)−p(j−1))/(p(j)+p(j−1)) [7]
where p(j) and p(j−1) represent dispersion factors for layers j and j−1, respectively. For light polarized in the parallel direction (i.e., the direction parallel to the plane of incidence), dispersion factor p(j) is given by the following:
p(j)=n(j)cos(θ(j)) [8]
where n(j) is the index of refraction of layer j, and θ(j) is the angle of incidence of the probe beam as it enters layer j. For light polarized in the in the perpendicular direction (i.e., perpendicular to the plane of incidence), dispersion factor p(j) is given by the following:
p(j)=cos(θ(j))/n(j) [9]
Dispersion factor p(j−1) for is calculated in a similar manner for the two light polarizations.
R BP(j)=(1−f)*(g p+(1+g p)*R BGL(j))+f*R BSF(j) [10a]
for p-polarized light (i.e., light polarized in the parallel (or transverse magnetic (TM)) direction), and:
R BS(j)=(1−f)*(g s+(1−g s)*R BGL(j))+f*R BSF(j) [10b]
for s-polarization (i.e., light polarized in the perpendicular (or transverse electric (TE)) direction), where RBP(j) is the lower reflectance of layer j for p-polarized light, RBS(j) is the lower reflectance of layer j for s-polarized light, RBGL(j) is the lower reflectance of layer j at a point above a grating line of grating layer j−1, and RBSF(j) is the lower reflectance of layer j at a point above a filler material portion of grating layer j−1, gp is the grating factor for p-polarized light, and gs is the grating factor for s-polarized light. Note that according to another embodiment of the invention, grating factors could be applied to the filler material terms RBSF(j) in Equations 10a and 10b.
g p =A p +B p/λ2 +C p/λ4 [11]
where Ap, Bp, and Cp are complex coefficients. According to another embodiment of the invention, the grating factors can even be functions of one or more of the attributes of interest (e.g., grating factors gp and gs can be functions of the thickness of the layer of interest).
R BGL(j)=(R FGL(j)+R TGL(j−1))/(1+R FGL(j)*R TGL(j−1)) [12]
where RFGL(j) is the interface Fresnel reflectance between layer j and a grating line in layer j−1, and RTGL(j−1) is the reflectance at the top of the grating line in layer j—1.
R TGL(j−1)=R BGL(j−1)exp(−4πi nGL(j−1)d(j−1)cos(θ(j−1))/λ) [13]
where RBGL(j−1) is the lower grating line reflectance of layer j−1, nGL(j−1) is the index of refraction the grating line in layer j−1, d(j−1) is the thickness of layer j−1, and θ(j−1) is the angle of incidence of the probe beam as it enters layer j−1.
n GL(j−1)=A GL(j−1)+B GL(j−1)/λ2 +C GL(j−1)/λ4 [14]
where AGL(j−1), BGL(j−1), and CGL(j−1) are Cauchy coefficients for index of refraction of the grating line material in layer j−1 and the wavelength λ of the probe beam. Note that various other equations can be used to define index of refraction. Note further that grating line index of refraction nGL(j−1) can also be replaced with a complex index of refraction NGL(j−1), as described above with respect to Equations 5 and 6.
R FGL(j)=(p(j)−p GL(j−1))/(p(j)+p GL(j−1)) [15]
where p(j) and pGL(j−1) represent dispersion factors for layer j and a grating line of layer j−1, respectively. Dispersion factor p(j) would be given by Equations 8 and 9 above, for light polarized in the parallel and perpendicular directions, respectively. Similarly, dispersion factor pGL(j−1) would be given by the following for light polarized in the parallel direction:
p GL(j−1)=n GL(j−1)cos(θ(j−1)) [16]
and by the following for light polarized in the in the perpendicular direction:
p GL(j−1)=cos(θ(j−1))/n GL(j−1) [17]
where p(j) and pGL(j−1) represent dispersion factors for layer j and a grating line of layer j−1, respectively, RFGL(j) is the interface Fresnel reflectance between layer j and a grating line in layer j−1, and RTGL(j−1) is the reflectance at the top of the grating line in layer j−1, and FTGL(j−1) is the transmittance at the top of the grating line in layer j−1, just as described above with respect to
F TGL(j−1)=F BGL(j−1)/exp (−2πi nGL(j−1)d(j−1)cos(θ(j−1))/λ) [19]
where RBGL(j−1) is the lower grating line reflectance of layer j−1, nGL(j−1) is the index of refraction the grating line in layer j−1, d(j−1) is the thickness of layer j−1, and θ(j−1) is the angle of incidence of the probe beam as it enters layer j−1, just as described above with respect to Equation 13.
Claims (42)
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